Chiral Quark Dynamics of Baryons

Amand Faessler, Tuebingen 1

Chiral Quark Dynamics of Baryons

Gutsche, Holstein, Lyubovitskij, + PhD students (Nicmorus,

Kuckei, Cheedket, Pumsa-ard, Khosonthongkee, Giacosa)

Amand Faessler, Tuebingen



Quantum Chromodynamics:

with:



1. P, C, T (exact)

2. Global (and local ) Gauge Invariance:

(exact)

for each flavor f

Effective Lagrangian for low Energies with the same Symmetries as QCD:



From this invariance follows:Conservation of the No quarks of flavor f;- baryon number- electric charge- Third compon. of Isospin- Strangeness- Charm …

3. Approximate Flavor Sym. all the same

u, d / SU(2) Isospin; u,d,s / SU(3)



4. Approximate Chiral Symmetry:

Current quark mass at QCD scale ~ 1 GeV

Current mass term:

Current quark mass term violates Chiral Symmetry



Low energy effective Lagrangian with correct Symmetries

Gluons and Quarks eliminated:

-> Chiral Perturbation theory

Gluons eliminated but with quarks:

-> Perturbative Chiral Quark Model (Manohar and Georgi)



Perturbative Chiral Quark Model A. Manohar and H. Georgi:

Nucl. Phys. B234 (1984) 189



Danger of Double Counting

in Chiral Quark Model :

Pseudoscalar Mesons as Goldstone

Bosons and as Quark-Antiquark States

Investigated by A. Manohar and H. Georgi:

Nucl. Phys. B234 (1984) 189Goldstone Bosons are the low lying pseudoscalar Mesons.

The quark-antiquark states lie very high.



Effective Lagrangian up to fourth order:The quark functions q, the quark momenta,

the constituent quark masses, and the chiral fields are of order 1: O(1).

Pseudoscalar meson masses, Meson momenta, electroweak potentials are of first order small.

Current quark masses, electric and magnetic field tensors Fare of second order small.



With:

Do not read this formula! On quark level suggested in leading order by Manohar and Georgi Nucl. Phys. B 234 (1984)189. On hadron level formulated by Gasser, Leutwyler,

Holstein, Meissner, Weise, Hemmert, Scherer and others up to fourth order.

Leading order

Up to fourth order in small quantities.



10 Parameters: mu ;ms ;g ;c2 ; c4 ;c5 ;e7 ;e8 ;e10 ;d10

Compositeness condition:

g( meson-quark) coupling;

constituent quarks

have mass in chiral limit



Parameters and counterterms: c6 ,e7 ,e8

fitted to the magnetic moments:

Parameters: c2 , c4 ,e10 ,d10 fitted to electric and magnetic radii of protons and neutrons:

With:



Formfactor of a single constituent bare quark q = u, d in the Nucleon at high energies can not calculated by chiral perturbation theory.

Nucleon expectation value of the bare constituent quark current.


Chiral Quark Dynamics of BaryonsAlternative approach: We use a simple Gaussian Function for the bare quarks (I. V. Anikin et. al. Z. Phys. C65(1995) 681):

k1E and k2E = Euclidian relative Jacobi momenta

B = 800 MeV

k1E

k2E



We dress now the bare quark current by the pseudoscalar meson cloud of pions, kaons and etas.



More diagrams:



Diagrams with vector mesons:



Connection with Vector Dominance Model



-

-

18 such type of diagrams included: Correction smaller than about 15 %

Pseudoscalar meson in flight not yet included. Small.

Counter terms

Single quark

Nucleon



Dressed Baryon Current



Effect of the pseudoscalar meson cloud on magnetic moments,

On electric and magnetic formfactors of protons and neutrons ,

On the N-Delta M1 transition and the ratio E2/M1 and C2/M1 for N -> .


Magnetic Diagonal and Transition Moments of the Baryon Octet in units: [ nm] =

FitEdelman; Blanpied et al.


Nucleon-Delta Transition GeV Data: S. Eidelman et al.; S.

Stave et al.; G. Blanpied et al.


Ratios of Coulomb and Electric Quadrupole over Magnetic Dipole for: Delta -> Nucleon +

Data: S. Stave et al.; N. F. Sparveris et al.; T. Popischil et al. ; D. Elsner et al. Eur. Phys. J. 27(2006) 91.

Valence quarks

Total: valence+cloud

Valence quarks

Total: valence+cloud


Connection beween Dirac, Pauli F1/2 and Sachs GE/M Formfactors

With:

DIRAC

Pauli


Electron-Proton Scattering and Rosenbluth

Separation of Sachs Formfactors: GpE and Gp

M



Chiral Quark Dynamics of Baryons Ratio :


Qualitative Explanation for the Electric Formfactor of the Proton:

+

proton proton

proton

proton

=

proton

=neutron

neutron

pion+

pion+

Fourier –Transf. with spherical Bessel-fct.:

Radius r

~85 % ~15 %

Bessel


Electric Formfactor of the Neutron

Cloud

Valence quarks

total

pion-

neutron

neutron

proton


Chiral Quark Dynamics of BaryonsMagnetic Proton Formfactor.


Chiral Quark Dynamics of BaryonsMagnetic Formfactor of the Neutron over the Dipole Formfactor


Electric over Magnetic Proton Formfactor

Rosenbluth Separation

Polarised e-beam plus polarized recoil protons

Data: SLAC: Walker et al.Phys.Rev.D (1994); Jefferson Lab Hall A :Punjabi et al. Phys. Rev. C (2005) and Gayou et al.P.R.L.


Summary:- Chiral Dynamics on quark level up to fourth order- Parameters and Counter Terms fixed to Magnetic

Moments (p, n, ), Radii and High Energy Behavior of Formfactors for Protons and Neutrons.

- Calculated Meson cloud Effects on Magnetic Moments of Baryon Octet

- Calculated meson cloud effects on N-transition- Effects of Pseudoscalar Meson Cloud on Formfactors.


The END


PUBLICATIONS:

1. A. Faessler, Th. Gutsche, V. E. Lyubovitskij, K. Pumsa-ard: Prog. Part. Nucl. Phys. 55 ( 2005) 12.

2. A. Faessler, Th. Gutsche, V. E. Lyubovitskij, K. Pumsa-ard: Phys. Rev. D73 (2006)114021

3. A. Faessler, Th. Gutsche, B. R. Holstein, E. Lyubovitskij: Phys. Rev. D74 (2006) 074010

Documents

Chiral Quark Dynamics of Baryons